abstract

Thirteen simple formulas describing the attenuation of Modified Mercalli (MM) intensity are compared to determine which best predicts observed values in North America. The equation (19) 
lnI=lnIo+a2b2lnΔc2Δ
based on the assumption that intensity is related to energy by the equation (12) 
I=kEP
appears to be the most useful, although it is not the most precise. P was found to be approximately 1/6, indicating that MM intensity is proportional to the sixth root of energy or the cube root of amplitude.

The United States and southern Canada are divided into three attenuation provinces: a San Andreas province with an energy absorption coefficient of 0.015/km, an Eastern province with an absorption coefficient of 0.0031/km and a Cordilleran province with an absorption coefficient of 0.0063/km.

The different rates of absorption can be explained as the result of slightly greater average focal depths in the East than in the West, although the data are too scattered to prove that this is the cause. Greater depth of focus, especially if low-angle faulting is involved, would explain the lack of surface displacement with eastern earthquakes.

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